Question: Simplify the following expression: $r = \dfrac{-3q^2 - 15q + 150}{q + 10} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ r =\dfrac{-3(q^2 + 5q - 50)}{q + 10} $ Then we factor the remaining polynomial: $q^2 + {5}q {-50} $ ${10} {-5} = {5}$ ${10} \times {-5} = {-50}$ $ (q + {10}) (q {-5}) $ This gives us a factored expression: $\dfrac{-3(q + {10}) (q {-5})}{q + 10}$ We can divide the numerator and denominator by $(q - 10)$ on condition that $q \neq -10$ Therefore $r = -3(q - 5); q \neq -10$